Exponential Decay and Regularity of Global Solutions for the 3D Navier–Stokes Equations Posed on Lipschitz and Smooth Domains

2020 ◽  
Vol 22 (3) ◽  
Author(s):  
N. A. Larkin ◽  
M. V. Padilha
Keyword(s):  
Exponential Decay ◽  
Stokes Equations ◽  
Global Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations

scholarly journals Decay of Strong Solutions for 4D Navier-Stokes Equations Posed on Lipschitz Domains

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
N. A. Larkin
Keyword(s):  
Exponential Decay ◽  
Stokes Equations ◽  
Global Solutions ◽  
Strong Solutions ◽  
Initial Boundary ◽  
Navier Stokes ◽  
Lipschitz Domains ◽  
Initial Boundary Value Problems ◽  
Navier Stokes Equations ◽  
Initial Boundary Value

Initial-boundary value problems for 4D Navier-Stokes equations posed on bounded and unbounded 4D parallelepipeds were considered. The existence and uniqueness of regular global solutions on bounded parallelepipeds and their exponential decay as well as the existence, uniqueness, and exponential decay of strong solutions on an unbounded parallelepiped have been established provided that initial data and domains satisfy some special conditions.

Global solutions for the Navier-Stokes equations in the rotational framework

2013 ◽  
Vol 357 (2) ◽  
pp. 727-741 ◽  
Author(s):  
Tsukasa Iwabuchi ◽  
Ryo Takada
Keyword(s):  
Stokes Equations ◽  
Global Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations

Exponential Decay in Time of Density of One-dimensional Quantum Navier-Stokes Equations

2018 ◽  
Vol 34 (4) ◽  
pp. 792-797
Author(s):  
Jian-wei Dong ◽  
Guang-pu Lou ◽  
Jun-hui Zhu ◽  
Yong Yang
Keyword(s):  
Exponential Decay ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
One Dimensional

scholarly journals From Boltzmann to incompressible Navier–Stokes in Sobolev spaces with polynomial weight

2018 ◽  
Vol 17 (01) ◽  
pp. 85-116 ◽  
Author(s):  
Marc Briant ◽  
Sara Merino-Aceituno ◽  
Clément Mouhot
Keyword(s):  
Boltzmann Equation ◽  
Knudsen Number ◽  
Exponential Decay ◽  
Sobolev Spaces ◽  
Stokes Equations ◽  
Linear Part ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
The Cauchy Problem ◽  
Global Equilibrium

We study the Boltzmann equation on the [Formula: see text]-dimensional torus in a perturbative setting around a global equilibrium under the Navier–Stokes linearization. We use a recent functional analysis breakthrough to prove that the linear part of the equation generates a [Formula: see text]-semigroup with exponential decay in Lebesgue and Sobolev spaces with polynomial weight, independently of the Knudsen number. Finally, we prove well-posedness of the Cauchy problem for the nonlinear Boltzmann equation in perturbative setting and an exponential decay for the perturbed Boltzmann equation, uniformly in the Knudsen number, in Sobolev spaces with polynomial weight. The polynomial weight is almost optimal. Furthermore, this result only requires derivatives in the space variable and allows to connect solutions to the incompressible Navier–Stokes equations in these spaces.

Sign in / Sign up

Export Citation Format

Share Document